Orthogonal polynomial decomposition for random fields with all moments (Q2002077)

The authors consider orthogonal polynomials in infinitely many variables and discuss the differences with orthogonal polynomials in \(d\) variables, especially with their relation with the theory of classical random variables with all moments taking values in a (finite or infinite dimensional) vector space. This is related to non-trivial extensions of quantum field theory. The main result of this paper is the proof of an infinite dimensional extension of Favard lemma (or spectral theorem for orthogonal polynomials).